The Spanish U21 star has made just 13 La Liga appearances for Madrid this term having seen fellow youngster Jese jump ahead of him in Carlo Ancelotti's plans.
Arsenal and north London rivals Tottenham were linked with a move for the young striker back in January.
Spurs were reportedly keen on taking Morata as part of Gareth Bale's record move to the Bernabeu - however it seems as though Arsenal now appear to be in the driving seat for his signature.
According to reports, the Gunners have made further enquiries over his availability in recent weeks, and have been quoted £25 million by Madrid to make the deal happen at the end of the season.
However they may now face a fight to land their man if reports are to be believed - Goal say that Inter Milan have identified the striker as the right man to lead their rejuvenated side next season.
Morata is out of contract in 2015 and Madrid may well be tempted to sell up this summer in order to receive a fee for him, rather than let him walk away for nothing next year.
The could encourage Arsenal to make a move for the youngster, who boss Arsene Wenger reportedly views as the solution to his striker problems.
As it stands Wenger can only call upon Olivier Giroud as his main source of goals, with Nicklas Bendtner and Yaya Sanogo as backup.
Juventus and Monaco are also said to be interested in the youngster.